Finite Group DatabasebetaFinite Group DatabasebetaOrder 1440.
564 conjugacy classes of subgroups; only the 178 normal subgroups are shown.
This group has 564 conjugacy classes of subgroups — too many to draw. Only its 178 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. C22×C32×C4×C5 | C2 | semidirect |
| 2. C2×C5×#638 | C2 | semidirect |
| 3. C2×C5×C4⋊(C3⋊D3) | C2 | semidirect |
| 4. C5×#3752 | C2 | semidirect |
| 5. C5×C4⋊(C3⋊Dic3) | C2 | semidirect |
| 15. #64139 | C5 | direct (N × H) |
| 16. C22×C3×C4×C5 | D3 | semidirect |
| 23. C22×C32×C5 | D4 | semidirect |
| 29. C32×C4×C5 | D4 | semidirect |
| 32. C22×C32×C4 | C2×C5 | semidirect |
| 33. C2×#638 | C2×C5 | semidirect |
| 34. C2×C4⋊(C3⋊D3) | C2×C5 | semidirect |
| 35. #3752 | C2×C5 | semidirect |
| 36. C4⋊(C3⋊Dic3) | C2×C5 | semidirect |
| 53. C22×C4×C5 | C3⋊D3 | semidirect |
| 66. C22×C3×C5 | D12 | semidirect |
| 72. C3×C4×C5 | #67 | semidirect |
| 74. C22×C3×C4 | C5×D3 | semidirect |
| 79. C32×C5 | #121 | semidirect |
| 90. C22×C32 | C5×D4 | semidirect |
| 96. C32×C4 | C5×D4 | semidirect |
| 117. C22×C5 | C4⋊(C3⋊D3) | semidirect |
| 121. C4×C5 | #638 | semidirect |
| 129. C22×C4 | C5×C3⋊D3 | semidirect |
| 132. C3×C5 | #930 | semidirect |
| 135. C22×C3 | C5×D12 | semidirect |
| 141. C3×C4 | C5×#67 | semidirect |
| 148. C32 | C5×#121 | semidirect |
| 162. C5 | #64139 | direct (N × H) |
| 168. C22 | C5×C4⋊(C3⋊D3) | semidirect |
| 172. C4 | C5×#638 | semidirect |
| 173. C3 | C5×#930 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C22×C32×C4×C5 | 2 |
| C2×C5×#638 | 2 |
| C2×C5×C4⋊(C3⋊D3) | 2 |
| C5×#3752 | 2 |
| C5×C4⋊(C3⋊Dic3) | 2 |
| C5×#930 | 3 |
| #64139 | 5 |